[tex]\bf \sqrt{8x^3+24x^2+18x}\implies \sqrt{2x(4x^2+12x+9)}
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\textit{now, let's check }
\begin{cases}
4x^2=2^2x^2\\
\qquad (2x)^2\\
9=3^2\\
12x=2(2x)(3)
\end{cases}\impliedby \textit{a perfect square trinomial}
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\sqrt{2x[(\underline{2x})^2+2(\underline{2x})(\underline{3})+\underline{3}^2]}\implies \sqrt{2x(2x+3)^2}
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\boxed{\pm (2x+3)\sqrt{2x}}[/tex]
